An implementation of matched filtering using the multi-dimensional Fourier transform

Details An implementation of matched filtering using the multi-dimensional Fourier transform An implementation of matched filtering using the multi-dimensional Fourier transform

Sep 2008

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008cqgra..25r4009m&link_type=abstract

Classical and Quantum Gravity, Volume 25, Issue 18, pp. 184009 (2008).

Physics

Scientific paper

We present an implementation of matched filtering comprised three basic steps: (1) compute a fast Fourier transform (FFT) of the data, (2) map the FFT to a (data independent) one-dimensional track in a multi-dimensional space, and (3) take an inverse multi-dimensional Fourier transform. In contrast to the standard approach, this method does not require the explicit use of template waveforms. This implementation was found as a byproduct of an exploration of sampling theory in the context of the template placement problem. We show that the latter problem can be completely mapped, in all its details, onto that of sampling an analog multi-dimensional random field, including the use of anti-aliasing before the acquisition of samples. The last point is non-trivial since the analog signal in question, namely the output of a template bank, does not physically exist unless it is computed.

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